Đặt \(a=\sqrt{x+4}+\sqrt{x-4}\left(a>0\right)\)
\(\Leftrightarrow a^2=x+4+x-4+2\sqrt{\left(x+4\right)\left(x-4\right)}\)
\(\Leftrightarrow a^2=2x+2\sqrt{x^2-16}\)
\(\Leftrightarrow a^2-12=2x-12+2\sqrt{x^2-16}\)
Do đó \(pt\Leftrightarrow a=a^2-12\)
\(\Leftrightarrow a^2-a-12=0\)
\(\Leftrightarrow\left(a-4\right)\left(a+3\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}a=4\\a=-3\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}\sqrt{x+4}+\sqrt{x-4}=4\\\sqrt{x+4}+\sqrt{x-4}=-3\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=5\\x=\varnothing\end{matrix}\right.\)
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